Method to estimate real-time rotation and translation of a target with a single x-ray imager

1. A method of real-time estimation of target rotation and translation in 6 degrees of freedom, comprising:

a. using an x-ray imager, during radiation treatment delivery, to acquire sequential images of the projected 2D positions of at least three fiducial markers implanted in a host, wherein a series of said fiducial markers in 2D images are determined;

b. determining, using an appropriately programmed computer, a covariance matrix of said fiducial marker locations and mean point fiducial marker locations by fitting a probability distribution function (PDF) to said series of fiducial marker locations in 2D images using a maximum likelihood estimation, wherein said series of fiducial markers location in 2D images are used to determine projected 3D points of said at least three fiducial markers in said host;

c. inputting said projected 3D points of said at least three fiducial markers to an iterative closest point (ICP) algorithm using said appropriately programmed computer to determine a real-time target rotation and translation about a center of mass of said at least three fiducial markers; and

d. outputting 3D locations of said at least three fiducial markers rotated around a right-left direction, an anterior-posterior direction, and a superior-inferior direction of said host.

2. The method of real-time estimation of target rotation and translation in 6 degrees of freedom according to claim 1 , wherein said ICP algorithm comprises:

a. creating pairing, using a nearest neighbor algorithm on said appropriately programmed computer, between a set of target points of at least three fiducial markers and a set of source points of said at least three fiducial markers using K nearest neighbors, wherein said source points are determined during a pretreatment arc that is used to build said PDF for said translation and said rotation estimation prior to turning said treatment beam on;

b. iteratively executing the following:

i. estimating a rotation parameter R and a translation parameter T of said at least three fiducial markers using a root mean square cost function;

ii. terminating the estimation of R and T when the change in a mean distance between said set of target points of said at least three fiducial markers and said set of source points of said at least three fiducial markers is below a threshold or at maximum iteration number;

iii. transforming said set of target points of said at least three fiducial markers using estimated parameters; and

iv. re-associating a new set of said target points of said at least three fiducial markers.

3. The method of real-time estimation of target rotation and translation in 6 degrees of freedom according to claim 1 , wherein said at least three fiducial markers are disposed in a non-linear arrangement.

4. The method of real-time estimation of target rotation and translation in 6 degrees of freedom according to claim 1 , wherein said source points of said at least three fiducial markers are generated at time t 1 by imaging said at least three fiducial markers using a kilovoltage imager mounted on a rotating gantry disposed to capture two-dimensional images of said at least three fiducial markers, wherein a source position of said at least three fiducial markers is estimated using a said PDF on said two-dimensional images of said at least three fiducial markers, wherein a translation and rotation of said at least three fiducial markers are estimated using said PDF.

5. The method of real-time estimation of target rotation and translation in 6 degrees of freedom according to claim 1 , wherein said target points of said at least three fiducial markers are generated at time t k by i) translating said source points of said at least three fiducial markers along an axis with an unknown transformation function using a translation vector T or ii) rotating said source points of said at least three fiducial markers around an axis with using a rotation matrix R or i) and ii), wherein a set of source points, one for each said fiducial marker, are denoted by Q=(q 1 , q 2 , . . . , q N ) and a set of target points, one for each said marker, are denoted by P=(p 1 , p 2 , . . . , p N ), wherein N is the number of fiducial markers, wherein when all said markers are translated and rotated by the same amount given by Q(P)=sRP+T+n, wherein s is a scaling factor, wherein n is Gaussian noise.

6. The method of real-time estimation of target rotation and translation in 6 degrees of freedom according to claim 5 , wherein said scaling factor is determined according to a change in an area defined by said at least three fiducial markers disposed in a non-linear arrangement captured in one 2D kilovoltage (kV) image compared to a subsequent 2D kilovoltage (kV) image.

7. The method of real-time estimation of target rotation and translation in 6 degrees of freedom according to claim 1 , wherein said at least three fiducial markers comprise an asymmetric shape.

8. The method of real-time estimation of target rotation and translation in 6 degrees of freedom according to claim 1 , wherein said ICP algorithm is executed between one 2D kilovoltage (kV) image and a next 2D kilovoltage (kV) image in a sequence.

9. The method of real-time estimation of target rotation and translation in 6 degrees of freedom according to claim 8 , wherein a frequency of said sequential 2D kilovoltage (kV) image is in a range of 0.1-100 Hz.

10. The method of real-time estimation of target rotation and translation in 6 degrees of freedom according to claim 1 , wherein said x-ray imager comprises a kilovoltage or megavoltage x-ray imager.

11. The method of real-time estimation of target rotation and translation in 6 degrees of freedom according to claim 1 , wherein said fiducial marker positions are used to give an estimate of target deformation.

12. The method of real-time estimation of target rotation and translation in 6 degrees of freedom according to claim 1 , wherein a treatment beam is applied to said target in real-time according to said 3D location of said at least three fiducial markers.